Second-order reconstruction of inflationary dynamics compatible with recent COBE data

A new method is applied to reconstruct the inflationary potential from a more phenomenological point of view. By using the more stringent nonlinear second order slow-roll approximation, we found, besides the power law inflation for n(s) < 1, an exact solution for which the spectral index is necessarily determined as n(s) similar or equal to 1.5. Part of these continuous and discrete spectra of the index fits within the 1 sigma range of recent COBE and CAT data. In the conformal frame, the inflation can be absorbed in a specific nonlinear curvature scalar Lagrangian parametrized by n(s) which is related to effective string models.